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Solving Fluid-Structure Interaction (FSI) problems using traditional methods is a big challenge in the field of numerical simulation. As a powerful multi-physical field coupled library, preCICE has a bright application prospect for solving…

Numerical Analysis · Mathematics 2024-04-30 Sifan Long , Xiaowei Guo , Xiaokang Fan , Canqun Yang

Monolithic preconditioners applied to the linear systems arising during the solution of the discretized incompressible Navier-Stokes equations are typically more robust than preconditioners based on incomplete block factorizations. Lower…

Numerical Analysis · Mathematics 2026-02-11 Alexander Heinlein , Axel Klawonn , Jascha Knepper , Lea Saßmannshausen

In the previous work, Zhang et al. proposed a multi-resolution smoothed particle hydrodynamics (SPH) method for fluid-structure interactions (FSI) with achieving an optimized computational efficiency meanwhile maintaining good numerical…

Fluid Dynamics · Physics 2022-05-03 Chi Zhang , Yujie Zhu , Xiangyu Hu

This work is on a user-friendly reduced basis method for solving a family of parametric PDEs by preconditioned Krylov subspace methods including the conjugate gradient method, generalized minimum residual method, and bi-conjugate gradient…

Numerical Analysis · Mathematics 2026-02-24 Yuwen Li , Ludmil T. Zikatanov , Cheng Zuo

We present a preconditioner for saddle point problems. The proposed preconditioner is extracted from a stationary iterative method which is convergent under a mild condition. Some properties of the preconditioner as well as the eigenvalues…

Numerical Analysis · Mathematics 2016-06-23 Davod Khojasteh Salkuyeh , Mohsen Masoudi

This paper presents an efficient Krylov subspace iterative solver for the three-dimensional (3D) Helmholtz equation with non-constant coefficients and absorbing boundary conditions, combining high-resolution compact schemes with low-order…

Numerical Analysis · Mathematics 2026-02-10 Yury Gryazin , Ron Gonzales , Xiaoye Sherry Li

The coupled Darcy-Stokes problem is widely used for modeling fluid transport in physical systems consisting of a porous part and a free part. In this work we consider preconditioners for monolitic solution algorithms of the coupled…

Numerical Analysis · Mathematics 2020-01-17 Karl Erik Holter , Miroslav Kuchta , Kent-Andre Mardal

We develop a simple algorithmic framework to solve large-scale symmetric positive definite linear systems. At its core, the framework relies on two components: (1) a norm-convergent iterative method (i.e. smoother) and (2) a preconditioner.…

Numerical Analysis · Mathematics 2013-02-18 Xiaozhe Hu , Shuhong Wu , Xiao-Hui Wu , Jinchao Xu , Chen-Song Zhang , Shiquan Zhang , Ludmil Zikatanov

This work considers the iterative solution of large-scale problems subject to non-symmetric matrices or operators arising in discretizations of (port-)Hamiltonian partial differential equations. We consider problems governed by an operator…

Numerical Analysis · Mathematics 2025-10-21 Volker Mehrmann , Manuel Schaller , Martin Stoll

The generalized Dryja--Smith--Widlund (GDSW) preconditioner is a two-level overlapping Schwarz domain decomposition (DD) preconditioner that couples a classical one-level overlapping Schwarz preconditioner with an energy-minimizing coarse…

Numerical Analysis · Mathematics 2023-04-12 Ichitaro Yamazaki , Alexander Heinlein , Sivasankaran Rajamanickam

A linearly implicit conservative difference scheme is applied to discretize the attractive coupled nonlinear Schr\"odinger equations with fractional Laplacian. Complex symmetric linear systems can be obtained, and the system matrices are…

Numerical Analysis · Mathematics 2023-10-19 Yan Cheng , Xi Yang

The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem,…

Numerical Analysis · Mathematics 2025-03-28 Daniele Boffi , Fabio Credali , Lucia Gastaldi , Simone Scacchi

In this paper, the authors constructed an auxiliary space multigrid preconditioner for the weak Galerkin finite element method for second-order diffusion equations, discretized on simplicial 2D or 3D meshes. The idea of the auxiliary space…

Numerical Analysis · Mathematics 2014-10-07 Long Chen , Junping Wang , Yanqiu Wang , Xiu Ye

We develop a three-dimensional Eulerian framework to simulate fluid-structure interaction (FSI) problems on a fixed Cartesian grid using the geometric volume-of-fluid (VOF) method. The coupled problem involves incompressible flow and…

Fluid Dynamics · Physics 2025-05-30 Soham Prajapati , Ali Fakhreddine , Krishnan Mahesh

Due to the wide separation of time scales in geophysical fluid dynamics, semi-implicit time integrators are commonly used in operational atmospheric forecast models. They guarantee the stable treatment of fast (acoustic and gravity) waves,…

Computational Physics · Physics 2020-12-30 Christopher Maynard , Thomas Melvin , Eike Hermann Müller

The recently introduced divergence-conforming B-spline discretizations allow the construction of smooth discrete velocity-pressure pairs for viscous incompressible flows that are at the same time inf-sup stable and divergence-free. When…

Numerical Analysis · Mathematics 2013-09-20 Adriano M. A. Cortes , Alvaro L. G. A. Coutinho

Solution methods for the nonlinear partial differential equation of the Rudin-Osher-Fatemi (ROF) and minimum-surface models are fundamental for many modern applications. Many efficient algorithms have been proposed. First order methods are…

Numerical Analysis · Mathematics 2022-08-03 Xue-Cheng Tai , Ragnar Winther , Xiaodi Zhang , Weiying Zheng

We aim to solve the incompressible Navier-Stokes equations within the complex microstructure of a porous material. Discretizing the equations on a fine grid using a staggered (e.g., marker-and-cell, mixed FEM) scheme results in a nonlinear…

Numerical Analysis · Mathematics 2025-10-28 Kangan Li , Yashar Mehmani

We propose an explicit partitioned (loosely coupled) scheme for fluid structure interaction (FSI) problems, specifically designed to achieve high computational efficiency in modern engineering simulations. The FSI problem under…

Numerical Analysis · Mathematics 2025-10-16 Shihan Guo , Ping Lin , Yifan Wang , Xiaohe Yue , Haibiao Zheng

We develop a robust and efficient iterative method for hyper-elastodynamics based on a novel continuum formulation recently developed. The numerical scheme is constructed based on the variational multiscale formulation and the…

Numerical Analysis · Mathematics 2019-02-20 Ju Liu , Alison L. Marsden